DFT and Falicov-Kimball Model Approach to $Cr_{9}$ Molecular Ring

Based on density functional theory (DFT) calculations, we present electronic and magnetic properties of nanometallic homo-nuclear chromium-based molecular rings $Cr_{9}F_{9}Cl_{2}(O_{2}C-C(CH_{3})_{3})_{17}$ recently synthesized. The magnetic moments are calculated, the spin density maps are discussed and the exchange interaction parameter is extracted. The complementary studies are carried out using the Falicov-Kimball model which reproduces very well the energy levels determined by different magnetic broken symmetry configurations obtained by DFT.